What are solid angles and how are they measured? How and in what units
can we determine the curvature of a sphere? What is the relation between
solid angles and the spherical curves they create when they intersect a
sphere whose center is the same as the vertex?

A student seeks help coding a spherical navigation spreadsheet program. Doctor Vogler helps him
develop an algorithm that accounts for the trigonometry involved, with each drawing
on archived conversations.

What is the name of a rectangle with two rounded ends, like a circle
with top and bottom evenly truncated? For example, an 'oval' racetrack
with two straightaways on opposite sides, parallel to each other and
both of the same length. I know that's not really an oval, but I'm
not sure what else to call it!